DengAI: Predicting Disease Spread

Background

Dengue

dengue: mosquito-borne diseae Dengue is a mosquito-borne disease. It occurs mainly in the tropical and subtropical parts of the world. Because it is transmitted by mosquitoes, the transmission of the disease is related to the climatic conditions and environmental variables such as precipitation and temperature. The disease is prevalent in Southeast Asia and Pacific Islands and epidemics of this disease are expected based on differences in climatic condtions. Nearly half a million cases of the dengue fever every year are reported in the Latin America, as reported by DataDriven.org.
dengue: competition

Data

DrivenData.org is an online platform that hosts several competitions throughout the year. The competition we decided to participate is DengAI: Predicting Disease Spread. dengue: competition This is an intermediate-level practice competition. Our task is to predict the number of dengue cases each week (in each location) based on environmental variables describing changes in temperature, precipitation, vegetation, and more.

The dataset was pulled from DrivenData.org. The link to dataset can be found here.The environmental data (features) has been collected by the U.S. Federal Government agencies - Centers for Disease Control (CDC) and Prevention to the National Oceanic and Atmospheric Administration (NOAA).

Objectives

Can we predict the number of dengue fever cases reported each week in San Juan, Puerto Rico and Iquitos, Peru? using environmental test data for a future date, from 2008 (week 18) till 2013 (week 13) for San Juan , and from 2010 (week 26) till 2013 (week 26) for Iquitos.

Aims

We used several supervised machine learning algorithms including Decision (Regression) Tree, Random Forest, Extreme Gradient Boosting, Partial Least Squares, and GLMNET for building the prediction model on the training set and compared their performance. Finally, the champion model was chosen for predicting outcomes on the future test dataset.

Prepare Data

Libraries

# install.packages("RCurl")
# install.packages("e1071")
# install.packages("caret")
# install.packages("doSNOW")
# install.packages("ipred")
# install.packages("xgboost")
# install.packages("dplyr")
# install.packages("tidyr")
# install.packages("naniar")
# install.packages("corrplot")
# install.packages("gbm")
# install.packages("mda")
# install.packages("psych")
# install.packages("kknn")
# install.packages("pls")
# install.packages("pamr")
# install.packages("mda")
# install.packages("rattle")
# install.packages("vtreat")
# install.packages("zoo")
library(RCurl)
## Loading required package: bitops
library(e1071)
library(caret)
## Loading required package: ggplot2
library(doSNOW)
## Loading required package: foreach
## Loading required package: iterators
## Loading required package: snow
library(ipred)
library(xgboost)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following object is masked from 'package:xgboost':
## 
##     slice
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(tidyr)
## 
## Attaching package: 'tidyr'
## The following object is masked from 'package:RCurl':
## 
##     complete
library(naniar)
library(corrplot)
## corrplot 0.84 loaded
library(psych)
## 
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
library(grid)
library(ggplot2)
library(kknn)
## 
## Attaching package: 'kknn'
## The following object is masked from 'package:caret':
## 
##     contr.dummy
library(pls)
## 
## Attaching package: 'pls'
## The following object is masked from 'package:corrplot':
## 
##     corrplot
## The following object is masked from 'package:caret':
## 
##     R2
## The following object is masked from 'package:stats':
## 
##     loadings
library(pamr)
## Loading required package: cluster
## Loading required package: survival
## 
## Attaching package: 'survival'
## The following object is masked from 'package:caret':
## 
##     cluster
## The following object is masked from 'package:rpart':
## 
##     solder
library(mda)
## Loading required package: class
## Loaded mda 0.4-10
library(rattle)
## Rattle: A free graphical interface for data science with R.
## Version 5.2.0 Copyright (c) 2006-2018 Togaware Pty Ltd.
## Type 'rattle()' to shake, rattle, and roll your data.
## 
## Attaching package: 'rattle'
## The following object is masked from 'package:xgboost':
## 
##     xgboost
library(vtreat)
library(glmnet)
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following object is masked from 'package:tidyr':
## 
##     expand
## Loaded glmnet 2.0-16
library(zoo)
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

Importing Data

#Importing Datasets Into the R-Console

# Importing features dataset using "getURL" method from the RCurl package. 
# This dataset contains information about the various features that can affect the incidence of the cases of dengue per week.
trfeat <- getURL("https://s3.amazonaws.com/drivendata/data/44/public/dengue_features_train.csv")
trfeat <-read.csv(text = trfeat)
names(trfeat)
##  [1] "city"                                 
##  [2] "year"                                 
##  [3] "weekofyear"                           
##  [4] "week_start_date"                      
##  [5] "ndvi_ne"                              
##  [6] "ndvi_nw"                              
##  [7] "ndvi_se"                              
##  [8] "ndvi_sw"                              
##  [9] "precipitation_amt_mm"                 
## [10] "reanalysis_air_temp_k"                
## [11] "reanalysis_avg_temp_k"                
## [12] "reanalysis_dew_point_temp_k"          
## [13] "reanalysis_max_air_temp_k"            
## [14] "reanalysis_min_air_temp_k"            
## [15] "reanalysis_precip_amt_kg_per_m2"      
## [16] "reanalysis_relative_humidity_percent" 
## [17] "reanalysis_sat_precip_amt_mm"         
## [18] "reanalysis_specific_humidity_g_per_kg"
## [19] "reanalysis_tdtr_k"                    
## [20] "station_avg_temp_c"                   
## [21] "station_diur_temp_rng_c"              
## [22] "station_max_temp_c"                   
## [23] "station_min_temp_c"                   
## [24] "station_precip_mm"
trfeat <- trfeat[, -c(4)]
dim(trfeat)
## [1] 1456   23
#Importing the training data features and labels 
trlabel <- getURL("https://s3.amazonaws.com/drivendata/data/44/public/dengue_labels_train.csv")
trlabel <- read.csv(text = trlabel)
names(trlabel)
## [1] "city"        "year"        "weekofyear"  "total_cases"
dim(trlabel)
## [1] 1456    4

The training feature set has 1456 rows and 23 columns. Features with the prefix ‘station’ imply the local weather station data; and those with prefix ‘reanalysis’ imply satellite data.

Merging

# Merging features and labels by their composite keys (i.e., a combination of 'city', 'year' and 'week of year')
dengue_train <- merge(trfeat, trlabel, by=c("city", "year", "weekofyear"))
names(dengue_train)
##  [1] "city"                                 
##  [2] "year"                                 
##  [3] "weekofyear"                           
##  [4] "ndvi_ne"                              
##  [5] "ndvi_nw"                              
##  [6] "ndvi_se"                              
##  [7] "ndvi_sw"                              
##  [8] "precipitation_amt_mm"                 
##  [9] "reanalysis_air_temp_k"                
## [10] "reanalysis_avg_temp_k"                
## [11] "reanalysis_dew_point_temp_k"          
## [12] "reanalysis_max_air_temp_k"            
## [13] "reanalysis_min_air_temp_k"            
## [14] "reanalysis_precip_amt_kg_per_m2"      
## [15] "reanalysis_relative_humidity_percent" 
## [16] "reanalysis_sat_precip_amt_mm"         
## [17] "reanalysis_specific_humidity_g_per_kg"
## [18] "reanalysis_tdtr_k"                    
## [19] "station_avg_temp_c"                   
## [20] "station_diur_temp_rng_c"              
## [21] "station_max_temp_c"                   
## [22] "station_min_temp_c"                   
## [23] "station_precip_mm"                    
## [24] "total_cases"
dim(dengue_train)
## [1] 1456   24

The training data features were merged with the training data labels (i.e., the total number of case per week) by their composite key (i.e., the combination of ‘city’, ‘year’, and ‘week of year’)

Missingness

anyNA(dengue_train)
## [1] TRUE
# Visualizing missing values for the training data
vis_miss(dengue_train)

gg_miss_var(dengue_train) + theme_minimal()

gg_miss_var(dengue_train, facet = city) + theme_gray()

ggplot(dengue_train, aes(x=ndvi_ne, y = total_cases)) + geom_point()
## Warning: Removed 194 rows containing missing values (geom_point).

ggplot(dengue_train, aes(x=ndvi_ne, y = total_cases)) + geom_miss_point()

Conclusion: Most of the missing values can be classified as ‘Missing Not At Random’.

Imputation

# Imputing missing values by using 'last-observation carried forward' method
dengue_train <- na.locf(dengue_train)
anyNA(dengue_train)
## [1] FALSE
vis_miss(dengue_train)

‘Last Observation Carried Forward’ method from library zoo was used to impute of the missing values in the training data.

Randomization

# Randomization of the training data
random_index <- sample(1:nrow(dengue_train), nrow(dengue_train))
random_train <- dengue_train[random_index, ]
names(random_train)
##  [1] "city"                                 
##  [2] "year"                                 
##  [3] "weekofyear"                           
##  [4] "ndvi_ne"                              
##  [5] "ndvi_nw"                              
##  [6] "ndvi_se"                              
##  [7] "ndvi_sw"                              
##  [8] "precipitation_amt_mm"                 
##  [9] "reanalysis_air_temp_k"                
## [10] "reanalysis_avg_temp_k"                
## [11] "reanalysis_dew_point_temp_k"          
## [12] "reanalysis_max_air_temp_k"            
## [13] "reanalysis_min_air_temp_k"            
## [14] "reanalysis_precip_amt_kg_per_m2"      
## [15] "reanalysis_relative_humidity_percent" 
## [16] "reanalysis_sat_precip_amt_mm"         
## [17] "reanalysis_specific_humidity_g_per_kg"
## [18] "reanalysis_tdtr_k"                    
## [19] "station_avg_temp_c"                   
## [20] "station_diur_temp_rng_c"              
## [21] "station_max_temp_c"                   
## [22] "station_min_temp_c"                   
## [23] "station_precip_mm"                    
## [24] "total_cases"
dim(random_train)
## [1] 1456   24
anyNA(random_train)
## [1] FALSE

Prediction Model

Parallel Processing

cl <- makeCluster(3, type = "SOCK")
registerDoSNOW(cl)

Hyperparameters

Grid

# Defining the tuning grid
grid <- expand.grid(eta = c(0.05, 0.5),
                         nrounds = c(70, 90),
                         max_depth = 1:6,
                         min_child_weight = c(1.0, 4),
                         colsample_bytree = c(0.5, 1),
                         gamma = c(5, 3, 0.1),
                         subsample = c(0.8, 1))

# grid <- expand.grid(eta = c(0.7),
#                          nrounds = c(10),
#                          max_depth = 3,
#                          min_child_weight = c(4),
#                          colsample_bytree = c(1),
#                          gamma = c(5),
#                          subsample = c(1))

trainControl

# Defining trainControl for the ML Algorithms
train.control <- trainControl(method = "repeatedcv",
                              number = 5,
                              repeats = 5,
                              search = "grid")

Algorithms

KNN

set.seed(45220)
model_kknn <- caret::train(total_cases ~ .,
                           data = random_train [,-c(2)],
                           type="prob",
                           method = "kknn",
                           tuneLength = 10,
                           preProcess = NULL,
                           trControl = train.control)
model_kknn
## k-Nearest Neighbors 
## 
## 1456 samples
##   22 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold, repeated 5 times) 
## Summary of sample sizes: 1165, 1166, 1164, 1165, 1164, 1165, ... 
## Resampling results across tuning parameters:
## 
##   kmax  RMSE      Rsquared   MAE     
##    5    34.62031  0.3652263  18.03672
##    7    34.07267  0.3760260  17.74447
##    9    33.94404  0.3801282  17.65169
##   11    33.99283  0.3804329  17.63109
##   13    34.03214  0.3797621  17.63088
##   15    34.05376  0.3793987  17.62855
##   17    34.05376  0.3793987  17.62855
##   19    34.05376  0.3793987  17.62855
##   21    34.05945  0.3792311  17.63026
##   23    34.05376  0.3793987  17.62855
## 
## Tuning parameter 'distance' was held constant at a value of 2
## 
## Tuning parameter 'kernel' was held constant at a value of optimal
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were kmax = 9, distance = 2 and
##  kernel = optimal.

GLMNET

# GLMNET Algorithm to Train The Prediction Model: generalized linear model via penalized maximum likelihood; the regulaization path is computed for elasticnet penalty at a grid of values for the regularization parameter lambada
set.seed(45220)
model_glmnet <- caret::train(total_cases ~ .,
                             data = random_train [,-c(2)],
                             method = "glmnet",
                             preProcess = NULL,
                             trControl = train.control)
model_glmnet
## glmnet 
## 
## 1456 samples
##   22 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold, repeated 5 times) 
## Summary of sample sizes: 1165, 1166, 1164, 1165, 1164, 1165, ... 
## Resampling results across tuning parameters:
## 
##   alpha  lambda      RMSE      Rsquared   MAE     
##   0.10   0.02833469  39.67484  0.1639065  21.88721
##   0.10   0.28334687  39.64924  0.1644656  21.75872
##   0.10   2.83346866  39.63550  0.1634235  20.89692
##   0.55   0.02833469  39.67039  0.1640119  21.86460
##   0.55   0.28334687  39.60990  0.1654590  21.52897
##   0.55   2.83346866  40.00117  0.1487682  20.35079
##   1.00   0.02833469  39.67162  0.1639042  21.85011
##   1.00   0.28334687  39.60029  0.1654297  21.33541
##   1.00   2.83346866  40.20430  0.1437450  20.19554
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.2833469.

Random Forest

x <- random_train[,2:22]

metric <- "MAE"
mtry <- sqrt(ncol(x))
model_rf <- caret::train(total_cases ~ ., 
                         data = random_train [,-c(2)],
                         method = "rf",
                         preProcess = NULL,
                         metric = metric,
                         tuneGrid = expand.grid(.mtry = mtry),
                         trControl = train.control)
model_rf
## Random Forest 
## 
## 1456 samples
##   22 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold, repeated 5 times) 
## Summary of sample sizes: 1166, 1165, 1165, 1164, 1164, 1165, ... 
## Resampling results:
## 
##   RMSE      Rsquared   MAE     
##   31.31542  0.4898275  17.13634
## 
## Tuning parameter 'mtry' was held constant at a value of 4.582576

Regression Tree

set.seed(123)
model_rpart <- caret::train(total_cases ~ ., data = random_train [,-c(2)],
                               method = "rpart",
                               preProcess = NULL,
                               trControl = train.control)
## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info =
## trainInfo, : There were missing values in resampled performance measures.
model_rpart
## CART 
## 
## 1456 samples
##   22 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold, repeated 5 times) 
## Summary of sample sizes: 1166, 1165, 1164, 1164, 1165, 1167, ... 
## Resampling results across tuning parameters:
## 
##   cp          RMSE      Rsquared   MAE     
##   0.05181416  36.13169  0.3174011  19.55505
##   0.07140796  37.56803  0.2656197  20.70815
##   0.18743688  41.17536  0.2012097  22.02441
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was cp = 0.05181416.
fancyRpartPlot(model_rpart$finalModel)

Partial Least Squares

set.seed(27)
model_pls <- caret::train(total_cases ~ .,
                          data = random_train [,-c(2)],
                          method = "pls",
                          preProcess = NULL,
                          trControl = train.control)
model_pls
## Partial Least Squares 
## 
## 1456 samples
##   22 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold, repeated 5 times) 
## Summary of sample sizes: 1165, 1164, 1164, 1167, 1164, 1164, ... 
## Resampling results across tuning parameters:
## 
##   ncomp  RMSE      Rsquared    MAE     
##   1      42.62615  0.01398885  22.77943
##   2      41.92215  0.05062343  22.33306
##   3      41.14722  0.08531144  22.01403
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was ncomp = 3.

Extreme Gradient Boosting

model_xgb <- caret::train(total_cases ~ .,
                          data = random_train [,-c(2)],
                          method = "xgbTree",
                          tuneGrid = grid,
                          trControl = train.control)
model_xgb
## eXtreme Gradient Boosting 
## 
## 1456 samples
##   22 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold, repeated 5 times) 
## Summary of sample sizes: 1164, 1166, 1164, 1165, 1165, 1164, ... 
## Resampling results across tuning parameters:
## 
##   eta   max_depth  gamma  colsample_bytree  min_child_weight  subsample
##   0.05  1          0.1    0.5               1                 0.8      
##   0.05  1          0.1    0.5               1                 0.8      
##   0.05  1          0.1    0.5               1                 1.0      
##   0.05  1          0.1    0.5               1                 1.0      
##   0.05  1          0.1    0.5               4                 0.8      
##   0.05  1          0.1    0.5               4                 0.8      
##   0.05  1          0.1    0.5               4                 1.0      
##   0.05  1          0.1    0.5               4                 1.0      
##   0.05  1          0.1    1.0               1                 0.8      
##   0.05  1          0.1    1.0               1                 0.8      
##   0.05  1          0.1    1.0               1                 1.0      
##   0.05  1          0.1    1.0               1                 1.0      
##   0.05  1          0.1    1.0               4                 0.8      
##   0.05  1          0.1    1.0               4                 0.8      
##   0.05  1          0.1    1.0               4                 1.0      
##   0.05  1          0.1    1.0               4                 1.0      
##   0.05  1          3.0    0.5               1                 0.8      
##   0.05  1          3.0    0.5               1                 0.8      
##   0.05  1          3.0    0.5               1                 1.0      
##   0.05  1          3.0    0.5               1                 1.0      
##   0.05  1          3.0    0.5               4                 0.8      
##   0.05  1          3.0    0.5               4                 0.8      
##   0.05  1          3.0    0.5               4                 1.0      
##   0.05  1          3.0    0.5               4                 1.0      
##   0.05  1          3.0    1.0               1                 0.8      
##   0.05  1          3.0    1.0               1                 0.8      
##   0.05  1          3.0    1.0               1                 1.0      
##   0.05  1          3.0    1.0               1                 1.0      
##   0.05  1          3.0    1.0               4                 0.8      
##   0.05  1          3.0    1.0               4                 0.8      
##   0.05  1          3.0    1.0               4                 1.0      
##   0.05  1          3.0    1.0               4                 1.0      
##   0.05  1          5.0    0.5               1                 0.8      
##   0.05  1          5.0    0.5               1                 0.8      
##   0.05  1          5.0    0.5               1                 1.0      
##   0.05  1          5.0    0.5               1                 1.0      
##   0.05  1          5.0    0.5               4                 0.8      
##   0.05  1          5.0    0.5               4                 0.8      
##   0.05  1          5.0    0.5               4                 1.0      
##   0.05  1          5.0    0.5               4                 1.0      
##   0.05  1          5.0    1.0               1                 0.8      
##   0.05  1          5.0    1.0               1                 0.8      
##   0.05  1          5.0    1.0               1                 1.0      
##   0.05  1          5.0    1.0               1                 1.0      
##   0.05  1          5.0    1.0               4                 0.8      
##   0.05  1          5.0    1.0               4                 0.8      
##   0.05  1          5.0    1.0               4                 1.0      
##   0.05  1          5.0    1.0               4                 1.0      
##   0.05  2          0.1    0.5               1                 0.8      
##   0.05  2          0.1    0.5               1                 0.8      
##   0.05  2          0.1    0.5               1                 1.0      
##   0.05  2          0.1    0.5               1                 1.0      
##   0.05  2          0.1    0.5               4                 0.8      
##   0.05  2          0.1    0.5               4                 0.8      
##   0.05  2          0.1    0.5               4                 1.0      
##   0.05  2          0.1    0.5               4                 1.0      
##   0.05  2          0.1    1.0               1                 0.8      
##   0.05  2          0.1    1.0               1                 0.8      
##   0.05  2          0.1    1.0               1                 1.0      
##   0.05  2          0.1    1.0               1                 1.0      
##   0.05  2          0.1    1.0               4                 0.8      
##   0.05  2          0.1    1.0               4                 0.8      
##   0.05  2          0.1    1.0               4                 1.0      
##   0.05  2          0.1    1.0               4                 1.0      
##   0.05  2          3.0    0.5               1                 0.8      
##   0.05  2          3.0    0.5               1                 0.8      
##   0.05  2          3.0    0.5               1                 1.0      
##   0.05  2          3.0    0.5               1                 1.0      
##   0.05  2          3.0    0.5               4                 0.8      
##   0.05  2          3.0    0.5               4                 0.8      
##   0.05  2          3.0    0.5               4                 1.0      
##   0.05  2          3.0    0.5               4                 1.0      
##   0.05  2          3.0    1.0               1                 0.8      
##   0.05  2          3.0    1.0               1                 0.8      
##   0.05  2          3.0    1.0               1                 1.0      
##   0.05  2          3.0    1.0               1                 1.0      
##   0.05  2          3.0    1.0               4                 0.8      
##   0.05  2          3.0    1.0               4                 0.8      
##   0.05  2          3.0    1.0               4                 1.0      
##   0.05  2          3.0    1.0               4                 1.0      
##   0.05  2          5.0    0.5               1                 0.8      
##   0.05  2          5.0    0.5               1                 0.8      
##   0.05  2          5.0    0.5               1                 1.0      
##   0.05  2          5.0    0.5               1                 1.0      
##   0.05  2          5.0    0.5               4                 0.8      
##   0.05  2          5.0    0.5               4                 0.8      
##   0.05  2          5.0    0.5               4                 1.0      
##   0.05  2          5.0    0.5               4                 1.0      
##   0.05  2          5.0    1.0               1                 0.8      
##   0.05  2          5.0    1.0               1                 0.8      
##   0.05  2          5.0    1.0               1                 1.0      
##   0.05  2          5.0    1.0               1                 1.0      
##   0.05  2          5.0    1.0               4                 0.8      
##   0.05  2          5.0    1.0               4                 0.8      
##   0.05  2          5.0    1.0               4                 1.0      
##   0.05  2          5.0    1.0               4                 1.0      
##   0.05  3          0.1    0.5               1                 0.8      
##   0.05  3          0.1    0.5               1                 0.8      
##   0.05  3          0.1    0.5               1                 1.0      
##   0.05  3          0.1    0.5               1                 1.0      
##   0.05  3          0.1    0.5               4                 0.8      
##   0.05  3          0.1    0.5               4                 0.8      
##   0.05  3          0.1    0.5               4                 1.0      
##   0.05  3          0.1    0.5               4                 1.0      
##   0.05  3          0.1    1.0               1                 0.8      
##   0.05  3          0.1    1.0               1                 0.8      
##   0.05  3          0.1    1.0               1                 1.0      
##   0.05  3          0.1    1.0               1                 1.0      
##   0.05  3          0.1    1.0               4                 0.8      
##   0.05  3          0.1    1.0               4                 0.8      
##   0.05  3          0.1    1.0               4                 1.0      
##   0.05  3          0.1    1.0               4                 1.0      
##   0.05  3          3.0    0.5               1                 0.8      
##   0.05  3          3.0    0.5               1                 0.8      
##   0.05  3          3.0    0.5               1                 1.0      
##   0.05  3          3.0    0.5               1                 1.0      
##   0.05  3          3.0    0.5               4                 0.8      
##   0.05  3          3.0    0.5               4                 0.8      
##   0.05  3          3.0    0.5               4                 1.0      
##   0.05  3          3.0    0.5               4                 1.0      
##   0.05  3          3.0    1.0               1                 0.8      
##   0.05  3          3.0    1.0               1                 0.8      
##   0.05  3          3.0    1.0               1                 1.0      
##   0.05  3          3.0    1.0               1                 1.0      
##   0.05  3          3.0    1.0               4                 0.8      
##   0.05  3          3.0    1.0               4                 0.8      
##   0.05  3          3.0    1.0               4                 1.0      
##   0.05  3          3.0    1.0               4                 1.0      
##   0.05  3          5.0    0.5               1                 0.8      
##   0.05  3          5.0    0.5               1                 0.8      
##   0.05  3          5.0    0.5               1                 1.0      
##   0.05  3          5.0    0.5               1                 1.0      
##   0.05  3          5.0    0.5               4                 0.8      
##   0.05  3          5.0    0.5               4                 0.8      
##   0.05  3          5.0    0.5               4                 1.0      
##   0.05  3          5.0    0.5               4                 1.0      
##   0.05  3          5.0    1.0               1                 0.8      
##   0.05  3          5.0    1.0               1                 0.8      
##   0.05  3          5.0    1.0               1                 1.0      
##   0.05  3          5.0    1.0               1                 1.0      
##   0.05  3          5.0    1.0               4                 0.8      
##   0.05  3          5.0    1.0               4                 0.8      
##   0.05  3          5.0    1.0               4                 1.0      
##   0.05  3          5.0    1.0               4                 1.0      
##   0.05  4          0.1    0.5               1                 0.8      
##   0.05  4          0.1    0.5               1                 0.8      
##   0.05  4          0.1    0.5               1                 1.0      
##   0.05  4          0.1    0.5               1                 1.0      
##   0.05  4          0.1    0.5               4                 0.8      
##   0.05  4          0.1    0.5               4                 0.8      
##   0.05  4          0.1    0.5               4                 1.0      
##   0.05  4          0.1    0.5               4                 1.0      
##   0.05  4          0.1    1.0               1                 0.8      
##   0.05  4          0.1    1.0               1                 0.8      
##   0.05  4          0.1    1.0               1                 1.0      
##   0.05  4          0.1    1.0               1                 1.0      
##   0.05  4          0.1    1.0               4                 0.8      
##   0.05  4          0.1    1.0               4                 0.8      
##   0.05  4          0.1    1.0               4                 1.0      
##   0.05  4          0.1    1.0               4                 1.0      
##   0.05  4          3.0    0.5               1                 0.8      
##   0.05  4          3.0    0.5               1                 0.8      
##   0.05  4          3.0    0.5               1                 1.0      
##   0.05  4          3.0    0.5               1                 1.0      
##   0.05  4          3.0    0.5               4                 0.8      
##   0.05  4          3.0    0.5               4                 0.8      
##   0.05  4          3.0    0.5               4                 1.0      
##   0.05  4          3.0    0.5               4                 1.0      
##   0.05  4          3.0    1.0               1                 0.8      
##   0.05  4          3.0    1.0               1                 0.8      
##   0.05  4          3.0    1.0               1                 1.0      
##   0.05  4          3.0    1.0               1                 1.0      
##   0.05  4          3.0    1.0               4                 0.8      
##   0.05  4          3.0    1.0               4                 0.8      
##   0.05  4          3.0    1.0               4                 1.0      
##   0.05  4          3.0    1.0               4                 1.0      
##   0.05  4          5.0    0.5               1                 0.8      
##   0.05  4          5.0    0.5               1                 0.8      
##   0.05  4          5.0    0.5               1                 1.0      
##   0.05  4          5.0    0.5               1                 1.0      
##   0.05  4          5.0    0.5               4                 0.8      
##   0.05  4          5.0    0.5               4                 0.8      
##   0.05  4          5.0    0.5               4                 1.0      
##   0.05  4          5.0    0.5               4                 1.0      
##   0.05  4          5.0    1.0               1                 0.8      
##   0.05  4          5.0    1.0               1                 0.8      
##   0.05  4          5.0    1.0               1                 1.0      
##   0.05  4          5.0    1.0               1                 1.0      
##   0.05  4          5.0    1.0               4                 0.8      
##   0.05  4          5.0    1.0               4                 0.8      
##   0.05  4          5.0    1.0               4                 1.0      
##   0.05  4          5.0    1.0               4                 1.0      
##   0.05  5          0.1    0.5               1                 0.8      
##   0.05  5          0.1    0.5               1                 0.8      
##   0.05  5          0.1    0.5               1                 1.0      
##   0.05  5          0.1    0.5               1                 1.0      
##   0.05  5          0.1    0.5               4                 0.8      
##   0.05  5          0.1    0.5               4                 0.8      
##   0.05  5          0.1    0.5               4                 1.0      
##   0.05  5          0.1    0.5               4                 1.0      
##   0.05  5          0.1    1.0               1                 0.8      
##   0.05  5          0.1    1.0               1                 0.8      
##   0.05  5          0.1    1.0               1                 1.0      
##   0.05  5          0.1    1.0               1                 1.0      
##   0.05  5          0.1    1.0               4                 0.8      
##   0.05  5          0.1    1.0               4                 0.8      
##   0.05  5          0.1    1.0               4                 1.0      
##   0.05  5          0.1    1.0               4                 1.0      
##   0.05  5          3.0    0.5               1                 0.8      
##   0.05  5          3.0    0.5               1                 0.8      
##   0.05  5          3.0    0.5               1                 1.0      
##   0.05  5          3.0    0.5               1                 1.0      
##   0.05  5          3.0    0.5               4                 0.8      
##   0.05  5          3.0    0.5               4                 0.8      
##   0.05  5          3.0    0.5               4                 1.0      
##   0.05  5          3.0    0.5               4                 1.0      
##   0.05  5          3.0    1.0               1                 0.8      
##   0.05  5          3.0    1.0               1                 0.8      
##   0.05  5          3.0    1.0               1                 1.0      
##   0.05  5          3.0    1.0               1                 1.0      
##   0.05  5          3.0    1.0               4                 0.8      
##   0.05  5          3.0    1.0               4                 0.8      
##   0.05  5          3.0    1.0               4                 1.0      
##   0.05  5          3.0    1.0               4                 1.0      
##   0.05  5          5.0    0.5               1                 0.8      
##   0.05  5          5.0    0.5               1                 0.8      
##   0.05  5          5.0    0.5               1                 1.0      
##   0.05  5          5.0    0.5               1                 1.0      
##   0.05  5          5.0    0.5               4                 0.8      
##   0.05  5          5.0    0.5               4                 0.8      
##   0.05  5          5.0    0.5               4                 1.0      
##   0.05  5          5.0    0.5               4                 1.0      
##   0.05  5          5.0    1.0               1                 0.8      
##   0.05  5          5.0    1.0               1                 0.8      
##   0.05  5          5.0    1.0               1                 1.0      
##   0.05  5          5.0    1.0               1                 1.0      
##   0.05  5          5.0    1.0               4                 0.8      
##   0.05  5          5.0    1.0               4                 0.8      
##   0.05  5          5.0    1.0               4                 1.0      
##   0.05  5          5.0    1.0               4                 1.0      
##   0.05  6          0.1    0.5               1                 0.8      
##   0.05  6          0.1    0.5               1                 0.8      
##   0.05  6          0.1    0.5               1                 1.0      
##   0.05  6          0.1    0.5               1                 1.0      
##   0.05  6          0.1    0.5               4                 0.8      
##   0.05  6          0.1    0.5               4                 0.8      
##   0.05  6          0.1    0.5               4                 1.0      
##   0.05  6          0.1    0.5               4                 1.0      
##   0.05  6          0.1    1.0               1                 0.8      
##   0.05  6          0.1    1.0               1                 0.8      
##   0.05  6          0.1    1.0               1                 1.0      
##   0.05  6          0.1    1.0               1                 1.0      
##   0.05  6          0.1    1.0               4                 0.8      
##   0.05  6          0.1    1.0               4                 0.8      
##   0.05  6          0.1    1.0               4                 1.0      
##   0.05  6          0.1    1.0               4                 1.0      
##   0.05  6          3.0    0.5               1                 0.8      
##   0.05  6          3.0    0.5               1                 0.8      
##   0.05  6          3.0    0.5               1                 1.0      
##   0.05  6          3.0    0.5               1                 1.0      
##   0.05  6          3.0    0.5               4                 0.8      
##   0.05  6          3.0    0.5               4                 0.8      
##   0.05  6          3.0    0.5               4                 1.0      
##   0.05  6          3.0    0.5               4                 1.0      
##   0.05  6          3.0    1.0               1                 0.8      
##   0.05  6          3.0    1.0               1                 0.8      
##   0.05  6          3.0    1.0               1                 1.0      
##   0.05  6          3.0    1.0               1                 1.0      
##   0.05  6          3.0    1.0               4                 0.8      
##   0.05  6          3.0    1.0               4                 0.8      
##   0.05  6          3.0    1.0               4                 1.0      
##   0.05  6          3.0    1.0               4                 1.0      
##   0.05  6          5.0    0.5               1                 0.8      
##   0.05  6          5.0    0.5               1                 0.8      
##   0.05  6          5.0    0.5               1                 1.0      
##   0.05  6          5.0    0.5               1                 1.0      
##   0.05  6          5.0    0.5               4                 0.8      
##   0.05  6          5.0    0.5               4                 0.8      
##   0.05  6          5.0    0.5               4                 1.0      
##   0.05  6          5.0    0.5               4                 1.0      
##   0.05  6          5.0    1.0               1                 0.8      
##   0.05  6          5.0    1.0               1                 0.8      
##   0.05  6          5.0    1.0               1                 1.0      
##   0.05  6          5.0    1.0               1                 1.0      
##   0.05  6          5.0    1.0               4                 0.8      
##   0.05  6          5.0    1.0               4                 0.8      
##   0.05  6          5.0    1.0               4                 1.0      
##   0.05  6          5.0    1.0               4                 1.0      
##   0.50  1          0.1    0.5               1                 0.8      
##   0.50  1          0.1    0.5               1                 0.8      
##   0.50  1          0.1    0.5               1                 1.0      
##   0.50  1          0.1    0.5               1                 1.0      
##   0.50  1          0.1    0.5               4                 0.8      
##   0.50  1          0.1    0.5               4                 0.8      
##   0.50  1          0.1    0.5               4                 1.0      
##   0.50  1          0.1    0.5               4                 1.0      
##   0.50  1          0.1    1.0               1                 0.8      
##   0.50  1          0.1    1.0               1                 0.8      
##   0.50  1          0.1    1.0               1                 1.0      
##   0.50  1          0.1    1.0               1                 1.0      
##   0.50  1          0.1    1.0               4                 0.8      
##   0.50  1          0.1    1.0               4                 0.8      
##   0.50  1          0.1    1.0               4                 1.0      
##   0.50  1          0.1    1.0               4                 1.0      
##   0.50  1          3.0    0.5               1                 0.8      
##   0.50  1          3.0    0.5               1                 0.8      
##   0.50  1          3.0    0.5               1                 1.0      
##   0.50  1          3.0    0.5               1                 1.0      
##   0.50  1          3.0    0.5               4                 0.8      
##   0.50  1          3.0    0.5               4                 0.8      
##   0.50  1          3.0    0.5               4                 1.0      
##   0.50  1          3.0    0.5               4                 1.0      
##   0.50  1          3.0    1.0               1                 0.8      
##   0.50  1          3.0    1.0               1                 0.8      
##   0.50  1          3.0    1.0               1                 1.0      
##   0.50  1          3.0    1.0               1                 1.0      
##   0.50  1          3.0    1.0               4                 0.8      
##   0.50  1          3.0    1.0               4                 0.8      
##   0.50  1          3.0    1.0               4                 1.0      
##   0.50  1          3.0    1.0               4                 1.0      
##   0.50  1          5.0    0.5               1                 0.8      
##   0.50  1          5.0    0.5               1                 0.8      
##   0.50  1          5.0    0.5               1                 1.0      
##   0.50  1          5.0    0.5               1                 1.0      
##   0.50  1          5.0    0.5               4                 0.8      
##   0.50  1          5.0    0.5               4                 0.8      
##   0.50  1          5.0    0.5               4                 1.0      
##   0.50  1          5.0    0.5               4                 1.0      
##   0.50  1          5.0    1.0               1                 0.8      
##   0.50  1          5.0    1.0               1                 0.8      
##   0.50  1          5.0    1.0               1                 1.0      
##   0.50  1          5.0    1.0               1                 1.0      
##   0.50  1          5.0    1.0               4                 0.8      
##   0.50  1          5.0    1.0               4                 0.8      
##   0.50  1          5.0    1.0               4                 1.0      
##   0.50  1          5.0    1.0               4                 1.0      
##   0.50  2          0.1    0.5               1                 0.8      
##   0.50  2          0.1    0.5               1                 0.8      
##   0.50  2          0.1    0.5               1                 1.0      
##   0.50  2          0.1    0.5               1                 1.0      
##   0.50  2          0.1    0.5               4                 0.8      
##   0.50  2          0.1    0.5               4                 0.8      
##   0.50  2          0.1    0.5               4                 1.0      
##   0.50  2          0.1    0.5               4                 1.0      
##   0.50  2          0.1    1.0               1                 0.8      
##   0.50  2          0.1    1.0               1                 0.8      
##   0.50  2          0.1    1.0               1                 1.0      
##   0.50  2          0.1    1.0               1                 1.0      
##   0.50  2          0.1    1.0               4                 0.8      
##   0.50  2          0.1    1.0               4                 0.8      
##   0.50  2          0.1    1.0               4                 1.0      
##   0.50  2          0.1    1.0               4                 1.0      
##   0.50  2          3.0    0.5               1                 0.8      
##   0.50  2          3.0    0.5               1                 0.8      
##   0.50  2          3.0    0.5               1                 1.0      
##   0.50  2          3.0    0.5               1                 1.0      
##   0.50  2          3.0    0.5               4                 0.8      
##   0.50  2          3.0    0.5               4                 0.8      
##   0.50  2          3.0    0.5               4                 1.0      
##   0.50  2          3.0    0.5               4                 1.0      
##   0.50  2          3.0    1.0               1                 0.8      
##   0.50  2          3.0    1.0               1                 0.8      
##   0.50  2          3.0    1.0               1                 1.0      
##   0.50  2          3.0    1.0               1                 1.0      
##   0.50  2          3.0    1.0               4                 0.8      
##   0.50  2          3.0    1.0               4                 0.8      
##   0.50  2          3.0    1.0               4                 1.0      
##   0.50  2          3.0    1.0               4                 1.0      
##   0.50  2          5.0    0.5               1                 0.8      
##   0.50  2          5.0    0.5               1                 0.8      
##   0.50  2          5.0    0.5               1                 1.0      
##   0.50  2          5.0    0.5               1                 1.0      
##   0.50  2          5.0    0.5               4                 0.8      
##   0.50  2          5.0    0.5               4                 0.8      
##   0.50  2          5.0    0.5               4                 1.0      
##   0.50  2          5.0    0.5               4                 1.0      
##   0.50  2          5.0    1.0               1                 0.8      
##   0.50  2          5.0    1.0               1                 0.8      
##   0.50  2          5.0    1.0               1                 1.0      
##   0.50  2          5.0    1.0               1                 1.0      
##   0.50  2          5.0    1.0               4                 0.8      
##   0.50  2          5.0    1.0               4                 0.8      
##   0.50  2          5.0    1.0               4                 1.0      
##   0.50  2          5.0    1.0               4                 1.0      
##   0.50  3          0.1    0.5               1                 0.8      
##   0.50  3          0.1    0.5               1                 0.8      
##   0.50  3          0.1    0.5               1                 1.0      
##   0.50  3          0.1    0.5               1                 1.0      
##   0.50  3          0.1    0.5               4                 0.8      
##   0.50  3          0.1    0.5               4                 0.8      
##   0.50  3          0.1    0.5               4                 1.0      
##   0.50  3          0.1    0.5               4                 1.0      
##   0.50  3          0.1    1.0               1                 0.8      
##   0.50  3          0.1    1.0               1                 0.8      
##   0.50  3          0.1    1.0               1                 1.0      
##   0.50  3          0.1    1.0               1                 1.0      
##   0.50  3          0.1    1.0               4                 0.8      
##   0.50  3          0.1    1.0               4                 0.8      
##   0.50  3          0.1    1.0               4                 1.0      
##   0.50  3          0.1    1.0               4                 1.0      
##   0.50  3          3.0    0.5               1                 0.8      
##   0.50  3          3.0    0.5               1                 0.8      
##   0.50  3          3.0    0.5               1                 1.0      
##   0.50  3          3.0    0.5               1                 1.0      
##   0.50  3          3.0    0.5               4                 0.8      
##   0.50  3          3.0    0.5               4                 0.8      
##   0.50  3          3.0    0.5               4                 1.0      
##   0.50  3          3.0    0.5               4                 1.0      
##   0.50  3          3.0    1.0               1                 0.8      
##   0.50  3          3.0    1.0               1                 0.8      
##   0.50  3          3.0    1.0               1                 1.0      
##   0.50  3          3.0    1.0               1                 1.0      
##   0.50  3          3.0    1.0               4                 0.8      
##   0.50  3          3.0    1.0               4                 0.8      
##   0.50  3          3.0    1.0               4                 1.0      
##   0.50  3          3.0    1.0               4                 1.0      
##   0.50  3          5.0    0.5               1                 0.8      
##   0.50  3          5.0    0.5               1                 0.8      
##   0.50  3          5.0    0.5               1                 1.0      
##   0.50  3          5.0    0.5               1                 1.0      
##   0.50  3          5.0    0.5               4                 0.8      
##   0.50  3          5.0    0.5               4                 0.8      
##   0.50  3          5.0    0.5               4                 1.0      
##   0.50  3          5.0    0.5               4                 1.0      
##   0.50  3          5.0    1.0               1                 0.8      
##   0.50  3          5.0    1.0               1                 0.8      
##   0.50  3          5.0    1.0               1                 1.0      
##   0.50  3          5.0    1.0               1                 1.0      
##   0.50  3          5.0    1.0               4                 0.8      
##   0.50  3          5.0    1.0               4                 0.8      
##   0.50  3          5.0    1.0               4                 1.0      
##   0.50  3          5.0    1.0               4                 1.0      
##   0.50  4          0.1    0.5               1                 0.8      
##   0.50  4          0.1    0.5               1                 0.8      
##   0.50  4          0.1    0.5               1                 1.0      
##   0.50  4          0.1    0.5               1                 1.0      
##   0.50  4          0.1    0.5               4                 0.8      
##   0.50  4          0.1    0.5               4                 0.8      
##   0.50  4          0.1    0.5               4                 1.0      
##   0.50  4          0.1    0.5               4                 1.0      
##   0.50  4          0.1    1.0               1                 0.8      
##   0.50  4          0.1    1.0               1                 0.8      
##   0.50  4          0.1    1.0               1                 1.0      
##   0.50  4          0.1    1.0               1                 1.0      
##   0.50  4          0.1    1.0               4                 0.8      
##   0.50  4          0.1    1.0               4                 0.8      
##   0.50  4          0.1    1.0               4                 1.0      
##   0.50  4          0.1    1.0               4                 1.0      
##   0.50  4          3.0    0.5               1                 0.8      
##   0.50  4          3.0    0.5               1                 0.8      
##   0.50  4          3.0    0.5               1                 1.0      
##   0.50  4          3.0    0.5               1                 1.0      
##   0.50  4          3.0    0.5               4                 0.8      
##   0.50  4          3.0    0.5               4                 0.8      
##   0.50  4          3.0    0.5               4                 1.0      
##   0.50  4          3.0    0.5               4                 1.0      
##   0.50  4          3.0    1.0               1                 0.8      
##   0.50  4          3.0    1.0               1                 0.8      
##   0.50  4          3.0    1.0               1                 1.0      
##   0.50  4          3.0    1.0               1                 1.0      
##   0.50  4          3.0    1.0               4                 0.8      
##   0.50  4          3.0    1.0               4                 0.8      
##   0.50  4          3.0    1.0               4                 1.0      
##   0.50  4          3.0    1.0               4                 1.0      
##   0.50  4          5.0    0.5               1                 0.8      
##   0.50  4          5.0    0.5               1                 0.8      
##   0.50  4          5.0    0.5               1                 1.0      
##   0.50  4          5.0    0.5               1                 1.0      
##   0.50  4          5.0    0.5               4                 0.8      
##   0.50  4          5.0    0.5               4                 0.8      
##   0.50  4          5.0    0.5               4                 1.0      
##   0.50  4          5.0    0.5               4                 1.0      
##   0.50  4          5.0    1.0               1                 0.8      
##   0.50  4          5.0    1.0               1                 0.8      
##   0.50  4          5.0    1.0               1                 1.0      
##   0.50  4          5.0    1.0               1                 1.0      
##   0.50  4          5.0    1.0               4                 0.8      
##   0.50  4          5.0    1.0               4                 0.8      
##   0.50  4          5.0    1.0               4                 1.0      
##   0.50  4          5.0    1.0               4                 1.0      
##   0.50  5          0.1    0.5               1                 0.8      
##   0.50  5          0.1    0.5               1                 0.8      
##   0.50  5          0.1    0.5               1                 1.0      
##   0.50  5          0.1    0.5               1                 1.0      
##   0.50  5          0.1    0.5               4                 0.8      
##   0.50  5          0.1    0.5               4                 0.8      
##   0.50  5          0.1    0.5               4                 1.0      
##   0.50  5          0.1    0.5               4                 1.0      
##   0.50  5          0.1    1.0               1                 0.8      
##   0.50  5          0.1    1.0               1                 0.8      
##   0.50  5          0.1    1.0               1                 1.0      
##   0.50  5          0.1    1.0               1                 1.0      
##   0.50  5          0.1    1.0               4                 0.8      
##   0.50  5          0.1    1.0               4                 0.8      
##   0.50  5          0.1    1.0               4                 1.0      
##   0.50  5          0.1    1.0               4                 1.0      
##   0.50  5          3.0    0.5               1                 0.8      
##   0.50  5          3.0    0.5               1                 0.8      
##   0.50  5          3.0    0.5               1                 1.0      
##   0.50  5          3.0    0.5               1                 1.0      
##   0.50  5          3.0    0.5               4                 0.8      
##   0.50  5          3.0    0.5               4                 0.8      
##   0.50  5          3.0    0.5               4                 1.0      
##   0.50  5          3.0    0.5               4                 1.0      
##   0.50  5          3.0    1.0               1                 0.8      
##   0.50  5          3.0    1.0               1                 0.8      
##   0.50  5          3.0    1.0               1                 1.0      
##   0.50  5          3.0    1.0               1                 1.0      
##   0.50  5          3.0    1.0               4                 0.8      
##   0.50  5          3.0    1.0               4                 0.8      
##   0.50  5          3.0    1.0               4                 1.0      
##   0.50  5          3.0    1.0               4                 1.0      
##   0.50  5          5.0    0.5               1                 0.8      
##   0.50  5          5.0    0.5               1                 0.8      
##   0.50  5          5.0    0.5               1                 1.0      
##   0.50  5          5.0    0.5               1                 1.0      
##   0.50  5          5.0    0.5               4                 0.8      
##   0.50  5          5.0    0.5               4                 0.8      
##   0.50  5          5.0    0.5               4                 1.0      
##   0.50  5          5.0    0.5               4                 1.0      
##   0.50  5          5.0    1.0               1                 0.8      
##   0.50  5          5.0    1.0               1                 0.8      
##   0.50  5          5.0    1.0               1                 1.0      
##   0.50  5          5.0    1.0               1                 1.0      
##   0.50  5          5.0    1.0               4                 0.8      
##   0.50  5          5.0    1.0               4                 0.8      
##   0.50  5          5.0    1.0               4                 1.0      
##   0.50  5          5.0    1.0               4                 1.0      
##   0.50  6          0.1    0.5               1                 0.8      
##   0.50  6          0.1    0.5               1                 0.8      
##   0.50  6          0.1    0.5               1                 1.0      
##   0.50  6          0.1    0.5               1                 1.0      
##   0.50  6          0.1    0.5               4                 0.8      
##   0.50  6          0.1    0.5               4                 0.8      
##   0.50  6          0.1    0.5               4                 1.0      
##   0.50  6          0.1    0.5               4                 1.0      
##   0.50  6          0.1    1.0               1                 0.8      
##   0.50  6          0.1    1.0               1                 0.8      
##   0.50  6          0.1    1.0               1                 1.0      
##   0.50  6          0.1    1.0               1                 1.0      
##   0.50  6          0.1    1.0               4                 0.8      
##   0.50  6          0.1    1.0               4                 0.8      
##   0.50  6          0.1    1.0               4                 1.0      
##   0.50  6          0.1    1.0               4                 1.0      
##   0.50  6          3.0    0.5               1                 0.8      
##   0.50  6          3.0    0.5               1                 0.8      
##   0.50  6          3.0    0.5               1                 1.0      
##   0.50  6          3.0    0.5               1                 1.0      
##   0.50  6          3.0    0.5               4                 0.8      
##   0.50  6          3.0    0.5               4                 0.8      
##   0.50  6          3.0    0.5               4                 1.0      
##   0.50  6          3.0    0.5               4                 1.0      
##   0.50  6          3.0    1.0               1                 0.8      
##   0.50  6          3.0    1.0               1                 0.8      
##   0.50  6          3.0    1.0               1                 1.0      
##   0.50  6          3.0    1.0               1                 1.0      
##   0.50  6          3.0    1.0               4                 0.8      
##   0.50  6          3.0    1.0               4                 0.8      
##   0.50  6          3.0    1.0               4                 1.0      
##   0.50  6          3.0    1.0               4                 1.0      
##   0.50  6          5.0    0.5               1                 0.8      
##   0.50  6          5.0    0.5               1                 0.8      
##   0.50  6          5.0    0.5               1                 1.0      
##   0.50  6          5.0    0.5               1                 1.0      
##   0.50  6          5.0    0.5               4                 0.8      
##   0.50  6          5.0    0.5               4                 0.8      
##   0.50  6          5.0    0.5               4                 1.0      
##   0.50  6          5.0    0.5               4                 1.0      
##   0.50  6          5.0    1.0               1                 0.8      
##   0.50  6          5.0    1.0               1                 0.8      
##   0.50  6          5.0    1.0               1                 1.0      
##   0.50  6          5.0    1.0               1                 1.0      
##   0.50  6          5.0    1.0               4                 0.8      
##   0.50  6          5.0    1.0               4                 0.8      
##   0.50  6          5.0    1.0               4                 1.0      
##   0.50  6          5.0    1.0               4                 1.0      
##   nrounds  RMSE      Rsquared   MAE     
##   70       37.82777  0.2819919  19.37694
##   90       37.12477  0.3086709  19.27975
##   70       37.89151  0.2850948  19.39178
##   90       37.22350  0.3090311  19.33065
##   70       37.78272  0.2845592  19.34623
##   90       37.10141  0.3094972  19.28549
##   70       37.93919  0.2798148  19.38077
##   90       37.24534  0.3056280  19.30668
##   70       37.42427  0.3218270  19.55344
##   90       36.49534  0.3574368  19.38267
##   70       37.68970  0.3201758  19.59150
##   90       36.79839  0.3583948  19.45964
##   70       37.37657  0.3236809  19.51262
##   90       36.44545  0.3584432  19.38637
##   70       37.68970  0.3201758  19.59150
##   90       36.79839  0.3583948  19.45964
##   70       37.80798  0.2841654  19.33050
##   90       37.04035  0.3132935  19.27667
##   70       37.86464  0.2879628  19.37387
##   90       37.20845  0.3105000  19.30637
##   70       37.82295  0.2832065  19.36594
##   90       37.11689  0.3094957  19.27888
##   70       37.88282  0.2855877  19.37219
##   90       37.16027  0.3137257  19.29751
##   70       37.34928  0.3247421  19.49173
##   90       36.45863  0.3569996  19.32727
##   70       37.68970  0.3201758  19.59150
##   90       36.79839  0.3583948  19.45964
##   70       37.40076  0.3211277  19.49857
##   90       36.44294  0.3603980  19.35004
##   70       37.68970  0.3201758  19.59150
##   90       36.79839  0.3583948  19.45964
##   70       37.77295  0.2840846  19.35853
##   90       37.08205  0.3104475  19.29282
##   70       37.89332  0.2854692  19.37200
##   90       37.20394  0.3096735  19.29717
##   70       37.80942  0.2822278  19.35016
##   90       37.01076  0.3147058  19.25891
##   70       37.85681  0.2879672  19.37188
##   90       37.16752  0.3131482  19.29610
##   70       37.39789  0.3231474  19.49872
##   90       36.48074  0.3568139  19.33047
##   70       37.68970  0.3201758  19.59150
##   90       36.79839  0.3583948  19.45964
##   70       37.37591  0.3220588  19.53677
##   90       36.44975  0.3615227  19.35728
##   70       37.68970  0.3201758  19.59150
##   90       36.79839  0.3583948  19.45964
##   70       32.04084  0.4630586  16.84608
##   90       31.56403  0.4678590  16.77064
##   70       31.67245  0.4722561  16.77096
##   90       31.36017  0.4742007  16.73624
##   70       31.75736  0.4706110  16.78111
##   90       31.30756  0.4743086  16.70323
##   70       31.70103  0.4700417  16.76856
##   90       31.38959  0.4721218  16.74666
##   70       32.14271  0.4510593  16.86001
##   90       31.87007  0.4559898  16.82967
##   70       32.25938  0.4478575  16.96416
##   90       31.97860  0.4530996  16.94474
##   70       32.18133  0.4507595  16.84844
##   90       31.95712  0.4540074  16.83703
##   70       32.25502  0.4488699  16.96517
##   90       31.97085  0.4540656  16.94488
##   70       31.76862  0.4686190  16.78314
##   90       31.42119  0.4712411  16.71091
##   70       31.68941  0.4722283  16.74897
##   90       31.41045  0.4729956  16.72421
##   70       31.77883  0.4716040  16.77155
##   90       31.35866  0.4744077  16.71869
##   70       31.77250  0.4685687  16.79532
##   90       31.43417  0.4714241  16.77204
##   70       32.28161  0.4466385  16.85987
##   90       32.00643  0.4500446  16.84081
##   70       32.25938  0.4478575  16.96416
##   90       31.97860  0.4530996  16.94474
##   70       32.18895  0.4497156  16.86830
##   90       31.89092  0.4542254  16.84307
##   70       32.25502  0.4488699  16.96517
##   90       31.97085  0.4540656  16.94488
##   70       31.80707  0.4706318  16.73016
##   90       31.30578  0.4757467  16.65561
##   70       31.67137  0.4688434  16.78470
##   90       31.38915  0.4712572  16.75951
##   70       31.74317  0.4739217  16.73303
##   90       31.33794  0.4763039  16.68450
##   70       31.68636  0.4682936  16.73697
##   90       31.43621  0.4694569  16.73356
##   70       32.15358  0.4517658  16.85536
##   90       31.89967  0.4554752  16.82110
##   70       32.25938  0.4478575  16.96416
##   90       31.97860  0.4530996  16.94474
##   70       32.22730  0.4474377  16.86616
##   90       31.92658  0.4525443  16.82461
##   70       32.25502  0.4488699  16.96517
##   90       31.97085  0.4540656  16.94488
##   70       29.91118  0.5145319  15.88893
##   90       29.61198  0.5176015  15.89537
##   70       29.64541  0.5188106  15.80850
##   90       29.45301  0.5203425  15.83925
##   70       30.33974  0.5041793  16.03576
##   90       30.05193  0.5057846  16.03330
##   70       29.90281  0.5106675  15.94496
##   90       29.69824  0.5133999  15.98507
##   70       30.86559  0.4829536  16.03090
##   90       30.59888  0.4897825  16.05649
##   70       31.03078  0.4803221  16.04455
##   90       30.76101  0.4881613  16.08797
##   70       31.00685  0.4802663  16.07642
##   90       30.81969  0.4846203  16.10592
##   70       31.28226  0.4712329  16.18844
##   90       31.11417  0.4754588  16.28708
##   70       30.00831  0.5104356  15.93358
##   90       29.71081  0.5132401  15.94499
##   70       29.60688  0.5193670  15.82678
##   90       29.32998  0.5234582  15.85561
##   70       30.34214  0.5010770  16.10020
##   90       30.13695  0.5024834  16.12063
##   70       29.90621  0.5102453  15.92619
##   90       29.74076  0.5116462  15.99471
##   70       30.73883  0.4890557  15.98265
##   90       30.47866  0.4953260  15.97378
##   70       31.03078  0.4803221  16.04455
##   90       30.76101  0.4881614  16.08797
##   70       30.93478  0.4811174  16.08590
##   90       30.71224  0.4857597  16.11046
##   70       31.28227  0.4712328  16.18844
##   90       31.11417  0.4754587  16.28708
##   70       29.92237  0.5129835  15.90761
##   90       29.58531  0.5171275  15.90513
##   70       29.69922  0.5152497  15.85170
##   90       29.48809  0.5178728  15.89616
##   70       30.42491  0.5001577  16.11647
##   90       30.07095  0.5043896  16.09521
##   70       29.86438  0.5117220  15.92868
##   90       29.66940  0.5135463  15.98155
##   70       30.78268  0.4886905  15.95056
##   90       30.48716  0.4953497  16.00138
##   70       31.03079  0.4803221  16.04455
##   90       30.75834  0.4882187  16.08594
##   70       31.02533  0.4778146  16.12814
##   90       30.84187  0.4814275  16.19393
##   70       31.28227  0.4712328  16.18844
##   90       31.11417  0.4754587  16.28708
##   70       29.26891  0.5311882  15.68051
##   90       29.01337  0.5337061  15.69718
##   70       28.75381  0.5442920  15.49553
##   90       28.55963  0.5463233  15.53960
##   70       29.65864  0.5201432  15.79289
##   90       29.43894  0.5212952  15.84015
##   70       29.26559  0.5257800  15.69026
##   90       29.14296  0.5262662  15.76651
##   70       30.29537  0.4990178  15.70305
##   90       30.10044  0.5041381  15.76623
##   70       30.74316  0.4882052  15.82510
##   90       30.55735  0.4945521  15.91844
##   70       30.50729  0.4909965  15.82001
##   90       30.36797  0.4942591  15.90402
##   70       30.76761  0.4821360  15.87126
##   90       30.62964  0.4876249  15.97806
##   70       29.14143  0.5353059  15.57908
##   90       28.84500  0.5378812  15.60079
##   70       29.02049  0.5360710  15.56758
##   90       28.82912  0.5374846  15.62123
##   70       29.67095  0.5207275  15.76826
##   90       29.44103  0.5218120  15.79239
##   70       29.23513  0.5276920  15.70571
##   90       29.16118  0.5262181  15.81228
##   70       30.33234  0.4991653  15.68310
##   90       30.07731  0.5058047  15.73633
##   70       30.75082  0.4879542  15.82579
##   90       30.56137  0.4943883  15.92329
##   70       30.70152  0.4874252  15.87084
##   90       30.51137  0.4921771  15.93029
##   70       30.76653  0.4820674  15.87071
##   90       30.62607  0.4876266  15.97236
##   70       29.37926  0.5280956  15.69947
##   90       29.17415  0.5290645  15.75889
##   70       29.01974  0.5363177  15.58929
##   90       28.81516  0.5380507  15.62452
##   70       29.41195  0.5279219  15.69518
##   90       29.19075  0.5293009  15.76638
##   70       29.39297  0.5234468  15.75202
##   90       29.23565  0.5239176  15.82411
##   70       30.39319  0.4961442  15.71434
##   90       30.16798  0.5020503  15.80016
##   70       30.74179  0.4882739  15.82108
##   90       30.55495  0.4947253  15.92027
##   70       30.62350  0.4902288  15.84920
##   90       30.51772  0.4922179  15.93235
##   70       30.77826  0.4817640  15.87626
##   90       30.63042  0.4873322  15.97922
##   70       28.90922  0.5424274  15.55442
##   90       28.63288  0.5445789  15.61099
##   70       28.80155  0.5410769  15.50420
##   90       28.64590  0.5413743  15.59072
##   70       29.23256  0.5321828  15.70871
##   90       29.01299  0.5342350  15.78879
##   70       29.23821  0.5275606  15.67793
##   90       29.10777  0.5282466  15.76815
##   70       30.15344  0.5034438  15.62406
##   90       30.00156  0.5074329  15.73690
##   70       30.58094  0.4944938  15.70968
##   90       30.43847  0.5006337  15.83635
##   70       30.22466  0.5020747  15.65898
##   90       30.12175  0.5046347  15.74510
##   70       30.92740  0.4802873  15.93823
##   90       30.85229  0.4829749  16.09238
##   70       28.96608  0.5396668  15.52257
##   90       28.67667  0.5431377  15.54570
##   70       28.86747  0.5405011  15.55276
##   90       28.65305  0.5425663  15.61787
##   70       29.21494  0.5337544  15.66604
##   90       29.00241  0.5351144  15.70675
##   70       29.11834  0.5324563  15.69812
##   90       28.95865  0.5333552  15.74410
##   70       30.24036  0.5009081  15.57632
##   90       30.05999  0.5057494  15.67594
##   70       30.64692  0.4939693  15.72485
##   90       30.45143  0.5009734  15.85459
##   70       30.34957  0.4952757  15.71265
##   90       30.22827  0.4985941  15.85201
##   70       30.92499  0.4804610  15.94433
##   90       30.83944  0.4835899  16.09431
##   70       28.99770  0.5369066  15.63625
##   90       28.72147  0.5397147  15.68612
##   70       28.66757  0.5440454  15.50945
##   90       28.47848  0.5457565  15.57110
##   70       29.41586  0.5264474  15.68737
##   90       29.22624  0.5266457  15.76681
##   70       29.14355  0.5283746  15.62838
##   90       29.08832  0.5268785  15.73805
##   70       30.15918  0.5028603  15.62881
##   90       29.98416  0.5082915  15.71674
##   70       30.59518  0.4943228  15.70398
##   90       30.45947  0.4994061  15.84614
##   70       30.26717  0.4997449  15.68654
##   90       30.16483  0.5018907  15.80272
##   70       30.91675  0.4806385  15.94242
##   90       30.82311  0.4840806  16.08037
##   70       28.96980  0.5392803  15.53378
##   90       28.68742  0.5431616  15.59169
##   70       28.45444  0.5531312  15.43971
##   90       28.25966  0.5548160  15.47779
##   70       29.31748  0.5310076  15.71944
##   90       29.09428  0.5320039  15.77117
##   70       29.02198  0.5336408  15.53982
##   90       28.81968  0.5359807  15.60797
##   70       30.29190  0.5019447  15.58392
##   90       30.14906  0.5065809  15.73277
##   70       30.95418  0.4848335  15.81919
##   90       30.86669  0.4899080  15.95953
##   70       30.09594  0.5052409  15.60729
##   90       30.04047  0.5072099  15.75346
##   70       30.95902  0.4815283  15.92864
##   90       30.88602  0.4848463  16.09364
##   70       29.05064  0.5366579  15.67394
##   90       28.80703  0.5381500  15.71959
##   70       28.82168  0.5412809  15.55559
##   90       28.67796  0.5412167  15.63323
##   70       29.28149  0.5317288  15.70839
##   90       29.10674  0.5321027  15.78679
##   70       29.18538  0.5275208  15.67262
##   90       29.05273  0.5278338  15.76274
##   70       30.24351  0.5025152  15.57606
##   90       30.06856  0.5079349  15.70265
##   70       30.92364  0.4855761  15.80213
##   90       30.79275  0.4917624  15.92563
##   70       30.32816  0.4983581  15.61775
##   90       30.23777  0.5003748  15.74568
##   70       30.91592  0.4826631  15.91854
##   90       30.86579  0.4853367  16.07698
##   70       28.97687  0.5389957  15.54904
##   90       28.74748  0.5407277  15.62020
##   70       28.64758  0.5476394  15.48186
##   90       28.44661  0.5494041  15.54590
##   70       29.16844  0.5345271  15.70814
##   90       28.98893  0.5348335  15.79042
##   70       28.76919  0.5392060  15.55157
##   90       28.65245  0.5391631  15.65005
##   70       30.24620  0.5031627  15.55518
##   90       30.15189  0.5061267  15.69750
##   70       30.91024  0.4859472  15.80449
##   90       30.78660  0.4917801  15.92879
##   70       30.34264  0.4994910  15.58293
##   90       30.25606  0.5016105  15.72886
##   70       30.86452  0.4837828  15.91376
##   90       30.82573  0.4862085  16.07515
##   70       31.76751  0.4503285  17.84056
##   90       31.53198  0.4568617  17.76577
##   70       31.25652  0.4672445  17.49753
##   90       31.11486  0.4704512  17.39981
##   70       31.73046  0.4503648  17.81527
##   90       31.69687  0.4519326  17.92255
##   70       31.31918  0.4666081  17.47564
##   90       31.15090  0.4700887  17.40696
##   70       31.41798  0.4587760  17.57319
##   90       31.41069  0.4580820  17.71292
##   70       31.16359  0.4716007  17.36697
##   90       31.05193  0.4742846  17.32707
##   70       31.32989  0.4620621  17.63307
##   90       31.34892  0.4610585  17.70703
##   70       31.16359  0.4716007  17.36697
##   90       31.05193  0.4742846  17.32707
##   70       31.67868  0.4524594  17.86011
##   90       31.50665  0.4561553  17.84854
##   70       31.23880  0.4683962  17.51011
##   90       31.13320  0.4705299  17.44606
##   70       31.69996  0.4522485  17.84669
##   90       31.54324  0.4551680  17.82610
##   70       31.29173  0.4659255  17.52476
##   90       31.14382  0.4696465  17.45210
##   70       31.46699  0.4589731  17.66810
##   90       31.37285  0.4612737  17.70977
##   70       31.16359  0.4716007  17.36697
##   90       31.05193  0.4742846  17.32707
##   70       31.35050  0.4625008  17.60769
##   90       31.33813  0.4610065  17.63842
##   70       31.16359  0.4716007  17.36697
##   90       31.05193  0.4742846  17.32707
##   70       31.61514  0.4554470  17.90344
##   90       31.52894  0.4561666  17.92304
##   70       31.29908  0.4668274  17.50095
##   90       31.19715  0.4690178  17.44908
##   70       31.65536  0.4535542  17.85130
##   90       31.61684  0.4541087  17.87428
##   70       31.25633  0.4679509  17.43664
##   90       31.11042  0.4709606  17.37228
##   70       31.32666  0.4622706  17.56729
##   90       31.22553  0.4650093  17.60708
##   70       31.16359  0.4716007  17.36697
##   90       31.05193  0.4742846  17.32707
##   70       31.37978  0.4613401  17.58318
##   90       31.30705  0.4621436  17.67297
##   70       31.16359  0.4716007  17.36697
##   90       31.05193  0.4742846  17.32707
##   70       32.09114  0.4522302  18.30094
##   90       32.35109  0.4485905  18.62136
##   70       31.34680  0.4724717  17.79388
##   90       31.43806  0.4707870  17.96606
##   70       32.46282  0.4453210  18.60268
##   90       32.60665  0.4435654  19.00546
##   70       31.92501  0.4540050  18.08031
##   90       32.10052  0.4511086  18.37038
##   70       33.04147  0.4345588  18.68662
##   90       33.17667  0.4346915  18.93063
##   70       31.35221  0.4747542  17.67883
##   90       31.37681  0.4767711  17.88142
##   70       33.23945  0.4323723  18.71017
##   90       33.37106  0.4314329  18.94947
##   70       31.84668  0.4617652  18.02875
##   90       32.04174  0.4598154  18.26717
##   70       32.09667  0.4517812  18.37210
##   90       32.14077  0.4541934  18.59644
##   70       31.39380  0.4707946  17.83540
##   90       31.51686  0.4713901  18.05838
##   70       32.60886  0.4402051  18.58268
##   90       32.80424  0.4373145  18.93425
##   70       32.21770  0.4483558  18.09129
##   90       32.37532  0.4453740  18.35143
##   70       32.23785  0.4545287  18.36984
##   90       32.55992  0.4493047  18.72154
##   70       31.35221  0.4747542  17.67883
##   90       31.37681  0.4767711  17.88142
##   70       33.11022  0.4261617  18.65769
##   90       33.54792  0.4188024  19.14293
##   70       31.84668  0.4617652  18.02875
##   90       32.04174  0.4598154  18.26717
##   70       32.86079  0.4311646  18.63203
##   90       32.98534  0.4309125  18.89841
##   70       31.46292  0.4721090  17.78487
##   90       31.58192  0.4727508  18.02246
##   70       32.58947  0.4390292  18.57343
##   90       32.73432  0.4387776  18.87660
##   70       31.44772  0.4654740  17.92669
##   90       31.60315  0.4649044  18.19957
##   70       32.40975  0.4510393  18.42551
##   90       32.56869  0.4503853  18.72272
##   70       31.35221  0.4747542  17.67883
##   90       31.37681  0.4767711  17.88142
##   70       33.35960  0.4234338  18.90996
##   90       33.52565  0.4220150  19.09055
##   70       31.84668  0.4617652  18.02875
##   90       32.04174  0.4598154  18.26717
##   70       32.33933  0.4536205  19.03811
##   90       32.51956  0.4504835  19.29520
##   70       31.14284  0.4751712  17.85337
##   90       31.22347  0.4738180  17.99747
##   70       32.56866  0.4381183  19.28497
##   90       32.71100  0.4365738  19.58140
##   70       31.80598  0.4585410  18.45225
##   90       31.95848  0.4557069  18.65310
##   70       33.13865  0.4420944  18.95088
##   90       33.27404  0.4401500  19.15875
##   70       32.26828  0.4647401  18.01123
##   90       32.43704  0.4621993  18.19334
##   70       33.59469  0.4302603  19.25777
##   90       33.71181  0.4288959  19.50564
##   70       32.45768  0.4504526  18.44346
##   90       32.47740  0.4503692  18.61953
##   70       32.77485  0.4369332  19.06851
##   90       32.97484  0.4346823  19.39180
##   70       31.68579  0.4698134  18.07099
##   90       31.78715  0.4685403  18.21675
##   70       32.76410  0.4383990  19.28162
##   90       32.84275  0.4384012  19.46279
##   70       32.03475  0.4501935  18.55004
##   90       32.21952  0.4460758  18.81557
##   70       33.38812  0.4362067  19.00135
##   90       33.64771  0.4317602  19.28317
##   70       32.24866  0.4661157  18.00441
##   90       32.37487  0.4642237  18.17039
##   70       33.90778  0.4100568  19.71882
##   90       34.13217  0.4061934  19.98749
##   70       32.45768  0.4504526  18.44346
##   90       32.47994  0.4503115  18.62199
##   70       32.17154  0.4525152  18.99064
##   90       32.29635  0.4508229  19.26412
##   70       31.27388  0.4734014  17.96446
##   90       31.31111  0.4731773  18.11228
##   70       32.90262  0.4329931  19.45596
##   90       33.15548  0.4286279  19.71208
##   70       32.23549  0.4526180  18.59549
##   90       32.39549  0.4500561  18.81481
##   70       32.96964  0.4413488  18.81825
##   90       33.05254  0.4411892  19.03768
##   70       32.24109  0.4664017  17.98590
##   90       32.38552  0.4639249  18.15559
##   70       34.00027  0.4150899  19.46190
##   90       34.18765  0.4134157  19.73250
##   70       32.45758  0.4504527  18.44326
##   90       32.47424  0.4505247  18.61821
##   70       32.92803  0.4348577  19.24984
##   90       33.02918  0.4329983  19.43374
##   70       31.85161  0.4592599  18.26291
##   90       31.90254  0.4583109  18.36179
##   70       33.52122  0.4210983  19.85807
##   90       33.59982  0.4201565  19.99960
##   70       32.27013  0.4458732  18.59939
##   90       32.31683  0.4450062  18.70602
##   70       33.42501  0.4361882  19.01361
##   90       33.50626  0.4345845  19.13433
##   70       32.34021  0.4662925  18.01214
##   90       32.41095  0.4649216  18.09411
##   70       33.71175  0.4212145  19.42128
##   90       33.81377  0.4191250  19.56650
##   70       32.52988  0.4492263  18.63235
##   90       32.59642  0.4477494  18.73045
##   70       32.68770  0.4393639  19.14881
##   90       32.80693  0.4371755  19.32279
##   70       31.81057  0.4556986  18.32965
##   90       31.88347  0.4542989  18.43853
##   70       32.98806  0.4351322  19.81585
##   90       33.11294  0.4326416  19.99489
##   70       32.44834  0.4439262  18.82924
##   90       32.54005  0.4420123  18.98094
##   70       33.91676  0.4258853  19.21887
##   90       33.96448  0.4255346  19.27439
##   70       32.40680  0.4668623  18.06481
##   90       32.41693  0.4670816  18.12825
##   70       34.06066  0.4089835  19.72188
##   90       34.09102  0.4093540  19.80716
##   70       32.56042  0.4482596  18.66822
##   90       32.63041  0.4469599  18.76029
##   70       32.94768  0.4340722  19.09807
##   90       33.02821  0.4326630  19.20647
##   70       32.07069  0.4524404  18.41986
##   90       32.17293  0.4501678  18.57273
##   70       33.71807  0.4167903  19.84939
##   90       33.82803  0.4144958  20.04336
##   70       31.85185  0.4534285  18.55753
##   90       31.97229  0.4510222  18.67888
##   70       33.11887  0.4426836  18.95591
##   90       33.20589  0.4406517  19.07601
##   70       32.43537  0.4678177  18.05122
##   90       32.49336  0.4663475  18.13978
##   70       34.15121  0.4139690  19.82788
##   90       34.22934  0.4123612  19.96636
##   70       32.56543  0.4481564  18.66446
##   90       32.63594  0.4466559  18.76049
##   70       33.04976  0.4245902  19.14329
##   90       33.09047  0.4236742  19.17597
##   70       31.20995  0.4720048  17.90849
##   90       31.21157  0.4722159  17.93420
##   70       33.30795  0.4223793  19.86632
##   90       33.34937  0.4215428  19.91651
##   70       31.71603  0.4588133  18.50698
##   90       31.75068  0.4580187  18.55345
##   70       33.63270  0.4290532  18.97098
##   90       33.64571  0.4289199  18.99795
##   70       32.16171  0.4673944  17.93516
##   90       32.16602  0.4673464  17.95537
##   70       34.12024  0.4193162  19.55925
##   90       34.14364  0.4191887  19.62838
##   70       32.93880  0.4420113  18.49566
##   90       32.96611  0.4416488  18.53051
##   70       33.44209  0.4196838  19.09750
##   90       33.45504  0.4196203  19.14237
##   70       31.78425  0.4620618  18.27238
##   90       31.79810  0.4618481  18.29400
##   70       33.85395  0.4177590  19.95817
##   90       33.89822  0.4170722  19.99594
##   70       32.04689  0.4452995  18.69874
##   90       32.08059  0.4447098  18.75473
##   70       33.67923  0.4246799  18.92980
##   90       33.70143  0.4239504  18.96703
##   70       32.17582  0.4684184  17.84993
##   90       32.18759  0.4681753  17.87083
##   70       33.81335  0.4229364  19.45648
##   90       33.83583  0.4228450  19.50216
##   70       32.90635  0.4428531  18.50678
##   90       32.92785  0.4425747  18.55420
##   70       32.66281  0.4392136  19.03792
##   90       32.67479  0.4392790  19.08226
##   70       31.69161  0.4582185  18.03936
##   90       31.70520  0.4580864  18.06509
##   70       33.59195  0.4146382  19.81658
##   90       33.60709  0.4143995  19.86180
##   70       32.14457  0.4496359  18.60679
##   90       32.16135  0.4494519  18.65545
##   70       33.70126  0.4236205  18.95683
##   90       33.71981  0.4232753  18.96857
##   70       32.02573  0.4706864  17.84829
##   90       32.02709  0.4708407  17.85936
##   70       34.17813  0.4081101  19.88424
##   90       34.21461  0.4072238  19.92249
##   70       32.91255  0.4436077  18.53766
##   90       32.92390  0.4434603  18.56138
##   70       33.15953  0.4223671  19.12529
##   90       33.16616  0.4222051  19.13897
##   70       32.12231  0.4434358  17.94486
##   90       32.11722  0.4435864  17.94451
##   70       33.85314  0.4110438  19.85219
##   90       33.87787  0.4105089  19.87248
##   70       32.48662  0.4358809  18.58528
##   90       32.49389  0.4357394  18.60931
##   70       33.71333  0.4309397  18.78966
##   90       33.72161  0.4308334  18.79807
##   70       32.57597  0.4569465  17.89440
##   90       32.58016  0.4568769  17.89640
##   70       34.28832  0.4033208  19.41733
##   90       34.29365  0.4031472  19.41621
##   70       32.78195  0.4439428  18.24119
##   90       32.78653  0.4438887  18.25707
##   70       32.83283  0.4333425  18.87593
##   90       32.83558  0.4332270  18.87748
##   70       31.72530  0.4562935  17.93604
##   90       31.73077  0.4561658  17.94301
##   70       33.91892  0.4100025  19.77663
##   90       33.92180  0.4100746  19.78424
##   70       32.22884  0.4524443  18.49897
##   90       32.23067  0.4524995  18.51571
##   70       33.78434  0.4196853  18.76070
##   90       33.78224  0.4197830  18.76447
##   70       32.52253  0.4575998  17.81695
##   90       32.52252  0.4575987  17.81705
##   70       34.52178  0.4095404  19.38608
##   90       34.51958  0.4095891  19.39700
##   70       32.78464  0.4457347  18.22292
##   90       32.78400  0.4458431  18.22819
##   70       33.61137  0.4100034  19.24579
##   90       33.60909  0.4100469  19.25084
##   70       32.66899  0.4355258  18.40549
##   90       32.66460  0.4356472  18.40526
##   70       34.30774  0.4000359  19.99375
##   90       34.29029  0.4005154  19.99960
##   70       32.38594  0.4456022  18.54524
##   90       32.38079  0.4458499  18.54956
##   70       33.28298  0.4391257  18.71238
##   90       33.28910  0.4389726  18.71685
##   70       32.60749  0.4536703  17.84117
##   90       32.60684  0.4536648  17.84002
##   70       33.80914  0.4243643  19.25179
##   90       33.81631  0.4243136  19.26381
##   70       32.78644  0.4459682  18.21723
##   90       32.79251  0.4458431  18.22258
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were nrounds = 90, max_depth = 6,
##  eta = 0.05, gamma = 0.1, colsample_bytree = 0.5, min_child_weight = 1
##  and subsample = 1.

Compare Prediction Models

models <- list( 
                xgb = model_xgb,
                rf = model_rf, 
                glmnet = model_glmnet, 
                kknn = model_kknn, 
                pls = model_pls,
                tree = model_rpart
)
resample_results <- resamples(models)
summary(resample_results)
## 
## Call:
## summary.resamples(object = resample_results)
## 
## Models: xgb, rf, glmnet, kknn, pls, tree 
## Number of resamples: 25 
## 
## MAE 
##            Min.  1st Qu.   Median     Mean  3rd Qu.     Max. NA's
## xgb    13.50315 14.62100 15.11518 15.47779 16.37681 18.29178    0
## rf     15.16717 16.41926 16.90462 17.13634 17.93979 19.30863    0
## glmnet 18.40796 19.85004 21.44573 21.33541 22.27389 24.21731    0
## kknn   14.89234 17.01223 17.44848 17.65169 18.27711 21.20296    0
## pls    17.78508 20.62333 21.57408 22.01403 23.60595 26.37508    0
## tree   17.14416 18.50250 19.44799 19.55505 20.34578 23.22488    0
## 
## RMSE 
##            Min.  1st Qu.   Median     Mean  3rd Qu.     Max. NA's
## xgb    21.54450 25.81589 28.09831 28.25966 30.12675 40.87635    0
## rf     25.14414 29.95393 31.56067 31.31542 33.51866 37.74072    0
## glmnet 29.70614 35.23244 39.78640 39.60029 43.03421 52.00255    0
## kknn   26.50537 32.33459 34.12527 33.94404 36.95560 41.65852    0
## pls    25.54762 36.56529 39.23736 41.14722 46.33878 56.72716    0
## tree   26.80192 33.04965 35.74302 36.13169 39.01360 46.48655    0
## 
## Rsquared 
##              Min.    1st Qu.     Median       Mean    3rd Qu.      Max.
## xgb    0.19464343 0.48715425 0.56913424 0.55481604 0.69049281 0.7488041
## rf     0.28064088 0.43486555 0.49470426 0.48982750 0.55706822 0.6506640
## glmnet 0.10322369 0.14979911 0.16790357 0.16542975 0.17804183 0.2117821
## kknn   0.20323670 0.29027887 0.37224539 0.38012815 0.45839184 0.5676154
## pls    0.04986561 0.07527861 0.08256124 0.08531144 0.09563748 0.1318126
## tree   0.06820792 0.24216320 0.32625110 0.31740106 0.40499125 0.5547894
##        NA's
## xgb       0
## rf        0
## glmnet    0
## kknn      0
## pls       0
## tree      0

Conclusion: The prediction model based on extreme gradient boosting algorithm is the champion model.

Prediction on Test Data

Import

# Importing the test data features on which the predictive model will be applied to predict total number of cases per week at a future date)
testset <- getURL("https://s3.amazonaws.com/drivendata/data/44/public/dengue_features_test.csv")
dengue_test <- read.csv(text=testset)
names(dengue_test)
##  [1] "city"                                 
##  [2] "year"                                 
##  [3] "weekofyear"                           
##  [4] "week_start_date"                      
##  [5] "ndvi_ne"                              
##  [6] "ndvi_nw"                              
##  [7] "ndvi_se"                              
##  [8] "ndvi_sw"                              
##  [9] "precipitation_amt_mm"                 
## [10] "reanalysis_air_temp_k"                
## [11] "reanalysis_avg_temp_k"                
## [12] "reanalysis_dew_point_temp_k"          
## [13] "reanalysis_max_air_temp_k"            
## [14] "reanalysis_min_air_temp_k"            
## [15] "reanalysis_precip_amt_kg_per_m2"      
## [16] "reanalysis_relative_humidity_percent" 
## [17] "reanalysis_sat_precip_amt_mm"         
## [18] "reanalysis_specific_humidity_g_per_kg"
## [19] "reanalysis_tdtr_k"                    
## [20] "station_avg_temp_c"                   
## [21] "station_diur_temp_rng_c"              
## [22] "station_max_temp_c"                   
## [23] "station_min_temp_c"                   
## [24] "station_precip_mm"
dim(dengue_test)
## [1] 416  24
dengue_test <- dengue_test[, -c(4)]
dim(dengue_test)
## [1] 416  23
# Visualizing missing values for the test data
anyNA(dengue_test)
## [1] TRUE
vis_miss(dengue_test)

Impute

dengue_test <- na.locf(dengue_test)
anyNA(dengue_test)
## [1] FALSE
vis_miss(dengue_test)

Predict

## Predicting total cases on test data
pred <- predict(model_rf, dengue_test)
dengue_test$total_cases <- round(pred, digits = 0)

Visualize

# Visualizing the time-series total cases on the test data
plot(dengue_test$total_cases)

Summary

# Summary of the predicted total cases
summary(dengue_test$total_cases)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    2.00   10.00   17.50   26.23   38.00  132.00

Exporting

#Entering the predicted 'total_cases' from the test-set into the submission form
Submitformat <- getURL("https://s3.amazonaws.com/drivendata/data/44/public/submission_format.csv")
submitformat <- read.csv(text=Submitformat)
submitformat$total_cases<- dengue_test$total_cases

# Exporting the output (total cases) to local drive as an Excel file
write.csv(submitformat, "D://STUDY//MSIS//DM//submit0407620xgb_send.csv", row.names = FALSE)

Current Ranking

dengueAR: our rank